APBRmetrics

**Eli W** · Joined: 01 Feb 2005 Posts: 401

I just put up a long post on my blog about diminishing returns and the value of offensive and defensive rebounds. It was prompted by a lot of the Wages of Wins discussion on this board and on Berri's blog. I'd be interested to hear any thoughts.

Diminishing Returns and the Value of Offensive and Defensive Rebounds
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Eli W. (formerly John Quincy)
CountTheBasket.com

Harold Almonte · Joined: 04 Aug 2006 Posts: 616

It's very strange that the team's Reb% slopes are very diferent than individual players, but very closed to ths SG's slopes. I can't find thwe why, but, can you make some table with the FGMissed (Rebounds chances) produced by those positions or heights?

Mountain · Joined: 13 Mar 2007 Posts: 1527

I'd be interested in learning more about how rebounding changed over time by height and position.

I came across the chart on page 10 of "A Starting Point for Analyzing Basketball Statistics" today showing the pretty sharp and steady decline of offensive rebounding over its 26 year period of study. How does that trend breakout to different positions and heights over your 33 year study? I be interested in seeing how your charts and tables for the most recent 5-10 years compare to past periods.

cherokee_ACB · Joined: 22 Mar 2006 Posts: 157

Take a look as well to this thread, in particular EdK's graph.

**Eli W** · Joined: 01 Feb 2005 Posts: 401

Ed Küpfer · Joined: 30 Dec 2004 Posts: 783 Location: Toronto

Mountain · Joined: 13 Mar 2007 Posts: 1527

I wonder if as league's tallest players got on average taller perimeter rebounding fell. And if the 3 pt revolution took the trend much farther.

Taller on average modern perimeter players might have greater ability to rebound more than their shorter predecessors but might not be positioned as well or make as much effort?

Speculation in wait of time period data.

Guy · Joined: 02 May 2007 Posts: 128

Nice work, Eli. I had some similar data I was going to post on the old WOW thread, but it seems like a better fit here now. The results are generally quite consistent with yours and Ed's, I think, and show an enormous diminishing returns effect.

I looked at rebounds by position, using 2006-07 data from 82 Games, and compared it both to rebounds at the other 4 positions on the same team and net rebounds for the team. Using positions rather than individual players has some advantages: MP is constant and it largely eliminates the good-rebounders-get-paired-with-weak-rebounders issue you raise. To deal with the underlying position differences, I converted the position values into rebounds above/below average for that position. So I get 150 "X" values, where X reflects the extra/fewer rebounds a team got from a given position.

Looking first at straight rebounds (position-adjusted), we see a negative correlation coefficient of -0.49 between one position's rebounds and the team's other positions. And regression indicates that for each additional rebound at a position, the other four positions lose 0.65 rebounds on average. If we look at the team total, each rebound at the position level translates into .27 team rebounds.

However, this actually understates the diminishing returns, because the shared rebounding opportunities (determined by pace and FG%) will tend to create positive correlations both among the five positions on a team and between a team and its opponents. So let's look at the real benefit to the team, defined as rebounds above average (Reb - .5*(Reb + OppReb)). Now we find that for each additional rebound gained at the position/player level, the team gains only .18 rebounds. In other words, WP and Win Score are crediting rebounds at more than 5 times their actual value.

Following Eli's lead, I also looked at Reb% by position, again normalized by position. Since we're now controlling well for opportunities, we expect to see a stronger relationship between position and team rebounds, and we do. But still, each additional 1% from a position increases team Reb% by only 0.25. (And decreases the Reb% for the other 4 positions by 0.75).

Clearly, this analysis is leaving out two potentially important dimensions: OReb vs. DReb (it seems clear that ORebs result more frequently in a real gain for the team), and differences by position (it may be that player Reb totals are more meaningful at some positions than others). But I think this helps set overall values, which coefficients for specific rebound types or positions should then be consistent with.

Finally, the SD for position-normed Reb% is .014 at the position/player level, and at the team level is just slightly higher at .016. This also tells us that there must be a huge negative correlation among teammates. If each player's rebounding was largely independent from that of his teammates, the team SD would then be sqrt(5*.014^2) = .032, or twice as large as it in fact is. (I think I misstated this gap as being much larger in an earlier post, because I had failed to control for player position, but the inter-dependence point stands).

BTW, if anyone wants the dataset, just send me a pm with your email address. I've sent it to both Berri and Jason, but neither have commented on it.

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Eli: one thing you might consider is position-adjusting or height-adjusting your data. This gives you much larger samples for your regressions (though at the cost of learning about position/height differences).

cherokee_ACB · Joined: 22 Mar 2006 Posts: 157

Guy · Joined: 02 May 2007 Posts: 128

Cherokee: The data I'm using is all rebounds from each position. If a team has a "good rebounding" center and plays "weaker rebounders" at other positions when he's on the floor, then the reverse must be true when backup centers are on the floor. So in that scenario, there should be no relationship between total Rebs at C and total Rebs at other positions -- at the position level, it's all a wash.

That still leaves the issue of team construction: in theory, once a team has 1 or 2 good rebounders they might be more willing to accept poor rebounders at other positions. But while there may be a little truth to this, I can't see how it can possibly account for the huge negative correlations among teammates we observe. It would require GMs not simply to undervalue rebounds (plausible), or even be indifferent to rebounding ability (not plausible), but to systematically seek out terrible rebounders whenever they already had some good rebounders (really not plausible).

Harold Almonte · Joined: 04 Aug 2006 Posts: 616

I think an advantage in using positions rather than individual height is, for example: a team has two 6'7" wings and a tweener 6'7" PF, the three with the same height, but defending at different floor position; one of them will have an advantage over the others that is not dependant of his height (let's remember that about 60% of rebounds caroms around the rim), and probably somebody will think that this advantaged player is more skilled (allthough the study shows almost no skill variation around this height, I think if you have a team with 5 6'7" players, one of them will rebound almost like an ordinary center because the floor position).

cherokee_ACB · Joined: 22 Mar 2006 Posts: 157

cherokee_ACB · Joined: 22 Mar 2006 Posts: 157

Eli, a couple of questions on the blog post:
- How did you compute player rebound rates?
- Do you include the 'worthy' team rebounds in your data, as BasketballValue does? I assume you do, but then you mention an average 73% DR rate, which comes from ignoring team rebounds (DR rate falls to 70% when team rebounds are added)

Guy · Joined: 02 May 2007 Posts: 128

Cherokee: I'm not sure I understand what you don't understand. Here's what I'm doing: I compare how many Rebs each team got at C (for example), to how many Rebs they got at the other 4 positions, or to the team's overall rebounds above average. For every extra reb at C, a team will get about .67 fewer reb's at the other 4 positions. And so on. Eli, in contrast, is looking at individual players, who might be paired with other players based on their respective rebounding ability.

As for the larger issue of team construction, I'm sure there's some truth but I basically don't buy it. I did the same exercise for points per shot (and turnovers), and do not find any diminishing returns there. GMs and coaches clearly don't say "I've got two good scorers, now let's find some guys who can't score to fill out our team." And to the extent they do say "there's no reason to pay for 3 great rebounders," I think they are recognizing the reality of diminishing returns, not creating the illusion of diminishing returns through their player selection.

**Eli W** · Joined: 01 Feb 2005 Posts: 401